WORST_CASE(?,O(1))
* Step 1: Sum.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict TRS:
            F(g(h(a(),b()),c()),d()) -> c3(F(.(b(),g(h(a(),b()),c())),d()))
            F(g(h(a(),b()),c()),d()) -> c4(F(c(),d'()))
            F(g(i(a(),b(),b'()),c()),d()) -> c1(F(.(b(),c()),d'()))
            F(g(i(a(),b(),b'()),c()),d()) -> c2(F(.(b'(),c()),d'()))
        - Weak TRS:
            f(g(h(a(),b()),c()),d()) -> if(e(),f(.(b(),g(h(a(),b()),c())),d()),f(c(),d'()))
            f(g(i(a(),b(),b'()),c()),d()) -> if(e(),f(.(b(),c()),d'()),f(.(b'(),c()),d'()))
        - Signature:
            {F/2,f/2} / {./2,a/0,b/0,b'/0,c/0,c1/1,c2/1,c3/1,c4/1,d/0,d'/0,e/0,g/2,h/2,i/3,if/3}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {F,f} and constructors {.,a,b,b',c,c1,c2,c3,c4,d,d',e,g,h
            ,i,if}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: DependencyPairs.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict TRS:
            F(g(h(a(),b()),c()),d()) -> c3(F(.(b(),g(h(a(),b()),c())),d()))
            F(g(h(a(),b()),c()),d()) -> c4(F(c(),d'()))
            F(g(i(a(),b(),b'()),c()),d()) -> c1(F(.(b(),c()),d'()))
            F(g(i(a(),b(),b'()),c()),d()) -> c2(F(.(b'(),c()),d'()))
        - Weak TRS:
            f(g(h(a(),b()),c()),d()) -> if(e(),f(.(b(),g(h(a(),b()),c())),d()),f(c(),d'()))
            f(g(i(a(),b(),b'()),c()),d()) -> if(e(),f(.(b(),c()),d'()),f(.(b'(),c()),d'()))
        - Signature:
            {F/2,f/2} / {./2,a/0,b/0,b'/0,c/0,c1/1,c2/1,c3/1,c4/1,d/0,d'/0,e/0,g/2,h/2,i/3,if/3}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {F,f} and constructors {.,a,b,b',c,c1,c2,c3,c4,d,d',e,g,h
            ,i,if}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          F#(g(h(a(),b()),c()),d()) -> c_1(F#(.(b(),g(h(a(),b()),c())),d()))
          F#(g(h(a(),b()),c()),d()) -> c_2(F#(c(),d'()))
          F#(g(i(a(),b(),b'()),c()),d()) -> c_3(F#(.(b(),c()),d'()))
          F#(g(i(a(),b(),b'()),c()),d()) -> c_4(F#(.(b'(),c()),d'()))
        Weak DPs
          f#(g(h(a(),b()),c()),d()) -> c_5(f#(.(b(),g(h(a(),b()),c())),d()),f#(c(),d'()))
          f#(g(i(a(),b(),b'()),c()),d()) -> c_6(f#(.(b(),c()),d'()),f#(.(b'(),c()),d'()))
        
        and mark the set of starting terms.
* Step 3: PredecessorEstimation.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            F#(g(h(a(),b()),c()),d()) -> c_1(F#(.(b(),g(h(a(),b()),c())),d()))
            F#(g(h(a(),b()),c()),d()) -> c_2(F#(c(),d'()))
            F#(g(i(a(),b(),b'()),c()),d()) -> c_3(F#(.(b(),c()),d'()))
            F#(g(i(a(),b(),b'()),c()),d()) -> c_4(F#(.(b'(),c()),d'()))
        - Weak DPs:
            f#(g(h(a(),b()),c()),d()) -> c_5(f#(.(b(),g(h(a(),b()),c())),d()),f#(c(),d'()))
            f#(g(i(a(),b(),b'()),c()),d()) -> c_6(f#(.(b(),c()),d'()),f#(.(b'(),c()),d'()))
        - Weak TRS:
            F(g(h(a(),b()),c()),d()) -> c3(F(.(b(),g(h(a(),b()),c())),d()))
            F(g(h(a(),b()),c()),d()) -> c4(F(c(),d'()))
            F(g(i(a(),b(),b'()),c()),d()) -> c1(F(.(b(),c()),d'()))
            F(g(i(a(),b(),b'()),c()),d()) -> c2(F(.(b'(),c()),d'()))
            f(g(h(a(),b()),c()),d()) -> if(e(),f(.(b(),g(h(a(),b()),c())),d()),f(c(),d'()))
            f(g(i(a(),b(),b'()),c()),d()) -> if(e(),f(.(b(),c()),d'()),f(.(b'(),c()),d'()))
        - Signature:
            {F/2,f/2,F#/2,f#/2} / {./2,a/0,b/0,b'/0,c/0,c1/1,c2/1,c3/1,c4/1,d/0,d'/0,e/0,g/2,h/2,i/3,if/3,c_1/1,c_2/1
            ,c_3/1,c_4/1,c_5/2,c_6/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {F#,f#} and constructors {.,a,b,b',c,c1,c2,c3,c4,d,d',e,g
            ,h,i,if}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,2,3,4}
        by application of
          Pre({1,2,3,4}) = {}.
        Here rules are labelled as follows:
          1: F#(g(h(a(),b()),c()),d()) -> c_1(F#(.(b(),g(h(a(),b()),c())),d()))
          2: F#(g(h(a(),b()),c()),d()) -> c_2(F#(c(),d'()))
          3: F#(g(i(a(),b(),b'()),c()),d()) -> c_3(F#(.(b(),c()),d'()))
          4: F#(g(i(a(),b(),b'()),c()),d()) -> c_4(F#(.(b'(),c()),d'()))
          5: f#(g(h(a(),b()),c()),d()) -> c_5(f#(.(b(),g(h(a(),b()),c())),d()),f#(c(),d'()))
          6: f#(g(i(a(),b(),b'()),c()),d()) -> c_6(f#(.(b(),c()),d'()),f#(.(b'(),c()),d'()))
* Step 4: RemoveWeakSuffixes.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            F#(g(h(a(),b()),c()),d()) -> c_1(F#(.(b(),g(h(a(),b()),c())),d()))
            F#(g(h(a(),b()),c()),d()) -> c_2(F#(c(),d'()))
            F#(g(i(a(),b(),b'()),c()),d()) -> c_3(F#(.(b(),c()),d'()))
            F#(g(i(a(),b(),b'()),c()),d()) -> c_4(F#(.(b'(),c()),d'()))
            f#(g(h(a(),b()),c()),d()) -> c_5(f#(.(b(),g(h(a(),b()),c())),d()),f#(c(),d'()))
            f#(g(i(a(),b(),b'()),c()),d()) -> c_6(f#(.(b(),c()),d'()),f#(.(b'(),c()),d'()))
        - Weak TRS:
            F(g(h(a(),b()),c()),d()) -> c3(F(.(b(),g(h(a(),b()),c())),d()))
            F(g(h(a(),b()),c()),d()) -> c4(F(c(),d'()))
            F(g(i(a(),b(),b'()),c()),d()) -> c1(F(.(b(),c()),d'()))
            F(g(i(a(),b(),b'()),c()),d()) -> c2(F(.(b'(),c()),d'()))
            f(g(h(a(),b()),c()),d()) -> if(e(),f(.(b(),g(h(a(),b()),c())),d()),f(c(),d'()))
            f(g(i(a(),b(),b'()),c()),d()) -> if(e(),f(.(b(),c()),d'()),f(.(b'(),c()),d'()))
        - Signature:
            {F/2,f/2,F#/2,f#/2} / {./2,a/0,b/0,b'/0,c/0,c1/1,c2/1,c3/1,c4/1,d/0,d'/0,e/0,g/2,h/2,i/3,if/3,c_1/1,c_2/1
            ,c_3/1,c_4/1,c_5/2,c_6/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {F#,f#} and constructors {.,a,b,b',c,c1,c2,c3,c4,d,d',e,g
            ,h,i,if}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:W:F#(g(h(a(),b()),c()),d()) -> c_1(F#(.(b(),g(h(a(),b()),c())),d()))
             
          
          2:W:F#(g(h(a(),b()),c()),d()) -> c_2(F#(c(),d'()))
             
          
          3:W:F#(g(i(a(),b(),b'()),c()),d()) -> c_3(F#(.(b(),c()),d'()))
             
          
          4:W:F#(g(i(a(),b(),b'()),c()),d()) -> c_4(F#(.(b'(),c()),d'()))
             
          
          5:W:f#(g(h(a(),b()),c()),d()) -> c_5(f#(.(b(),g(h(a(),b()),c())),d()),f#(c(),d'()))
             
          
          6:W:f#(g(i(a(),b(),b'()),c()),d()) -> c_6(f#(.(b(),c()),d'()),f#(.(b'(),c()),d'()))
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          6: f#(g(i(a(),b(),b'()),c()),d()) -> c_6(f#(.(b(),c()),d'()),f#(.(b'(),c()),d'()))
          5: f#(g(h(a(),b()),c()),d()) -> c_5(f#(.(b(),g(h(a(),b()),c())),d()),f#(c(),d'()))
          4: F#(g(i(a(),b(),b'()),c()),d()) -> c_4(F#(.(b'(),c()),d'()))
          3: F#(g(i(a(),b(),b'()),c()),d()) -> c_3(F#(.(b(),c()),d'()))
          2: F#(g(h(a(),b()),c()),d()) -> c_2(F#(c(),d'()))
          1: F#(g(h(a(),b()),c()),d()) -> c_1(F#(.(b(),g(h(a(),b()),c())),d()))
* Step 5: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            F(g(h(a(),b()),c()),d()) -> c3(F(.(b(),g(h(a(),b()),c())),d()))
            F(g(h(a(),b()),c()),d()) -> c4(F(c(),d'()))
            F(g(i(a(),b(),b'()),c()),d()) -> c1(F(.(b(),c()),d'()))
            F(g(i(a(),b(),b'()),c()),d()) -> c2(F(.(b'(),c()),d'()))
            f(g(h(a(),b()),c()),d()) -> if(e(),f(.(b(),g(h(a(),b()),c())),d()),f(c(),d'()))
            f(g(i(a(),b(),b'()),c()),d()) -> if(e(),f(.(b(),c()),d'()),f(.(b'(),c()),d'()))
        - Signature:
            {F/2,f/2,F#/2,f#/2} / {./2,a/0,b/0,b'/0,c/0,c1/1,c2/1,c3/1,c4/1,d/0,d'/0,e/0,g/2,h/2,i/3,if/3,c_1/1,c_2/1
            ,c_3/1,c_4/1,c_5/2,c_6/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {F#,f#} and constructors {.,a,b,b',c,c1,c2,c3,c4,d,d',e,g
            ,h,i,if}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(1))